Pages

Monday, July 15, 2013

Philosophy of Religion, Part 5: Fine-Tuning, Part 2

(See part 1 for readings)
Now we get to the Big Topic: the multiple universe hypothesis, which is the most prominent rival explanation to the God hypothesis. There are so many universes, the reasoning goes, that one of them was bound to be habitable to life. Several approaches can be taken:

The Mathematical Universe Hypothesis - all mathematical structures exist, so life was certain to exist in some substructure. Variants of this theory prefer some types of mathematical structures to others, in order to cut down on the sheer number of things which exist - for example, one variant hold that all Turing Computable structures exist, but that other mathematical structures only exist as formalisms.

Similar to the mathematical universe hypothesis is the modal realist hypothesis, famously proposed by philosopher David Lewis (albeit not in the context of fine-tuning arguments, but rather as a curiosity in the field of ontology). In modal logic there are entities called metaphysically possible worlds. Modal realism holds that all metaphysically possible worlds exist as actual worlds - and our universe was bound to be one of the metaphysically possible worlds.

Various multiverse theories derived from and inspired by physics, such as the hypothesis (from string theory?) that there are 10^500 universes with different fundamental parameters.

Hypotheses (1) and (2) are strongly disputed by philosophers. I rather like both of them, although when you work out the details, it's rather hard to pin down precisely how all of mathematics exists (there are, after all, competing axiom systems, plus Gödel's incompleteness theorems, plus the fact that there can be no set of all sets), and how, exactly, we can tell the difference between metaphysically and epistemically possible worlds, much less be justified in so drastically expanding our ontology?\begin{Slight Digression}
The benefit of (1) and (2) is that there is no problem of fine-tuning if they are true. In fact, in what I would dub the "Pervasive Anthropic Principle," nothing we observe should ever be surprising to us - if perfect copies of the Titanic started materializing and falling from the sky due to pure quantum randomness, then despite the sheer unlikeliness of this event, we could just say, "ah, well, someone was bound find themselves in a universe where this happened, so it might as well be us". Major criticisms of (1) and (2) point out precisely this fact - it seems to undermine our every ability to make inferences about the world. But in response, I would say that this is not so - it's all a matter of Bayesian reasoning. Given that we find ourselves in this fairly reasonable and orderly universe, what is the probability that the future will continue to be fairly ordinary (meaning, roughly, that absurd things don't start materializing out of quantum randomness)? Very, very high, because ordinary universes vastly outnumber the extraordinary ones (assuming a finite number of possible states). If something extraordinary does happen, then by Bayesian reasoning, it is much more likely to have a hidden ordinary cause than to be a brute property of the universe we find ourselves in. Thus, ordinary reasoning is saved from the pervasive anthropic principle. But then other problems crop up - does this reasoning still work if there are infinite possible states? And there is still the extraordinarily counterintuitive fact that somewhere, there is a universe in which Titanics materialize everywhere, wreaking havoc, and the poor inhabitants of this universe, with their own Bayesian reasoning, simply cannot figure out why. Potential solutions to this problem would limit the number and types of universes which can exist, but then why these particular limits, rather than anything else? So, in summary, (1) and (2) are philosophical curiosities that have potentially great explanatory power, but possibly far too much for their own good.\end{Slight Digression}
So for now we limit ourselves to various multiverse scenarios inspired by physics, noting that inferences to such multiverses are more philosophical rather than scientific in nature (since we do not seem to be capable of detecting other universes if they exist). In his essay "Anthropic Bias," philosopher Nick Bostrom explores many of the nuances of reasoning from fine-tuning, and unsurprisingly concludes that fine tuning can indeed provide Bayesian evidence for the existence of a multiverse, conditional on the weight of the prior probabilities. As he neatly put it,

"Does fine-tuning cry out for explanation? Does it give support to the multiverse hypothesis? Beginning with the latter question, we should say: Yes, to the extent that multiverse theories are simpler, more elegant, (and therefore able to claim a higher prior probability) than any rival theories that are compatible with what we observe."

But there are several potential problems with the multiverse hypothesis.

By postulating many entities, the multiverse hypothesis violates Occam's razor, and its prior probability ought to be severely penalized for its lack of simplicity.

Why didn't we find ourselves in a different universe? (A variant on the "pervasive anthropic principle" question in the digression above - see discussion below).

There is no scientific evidence of a multiverse

What if the multiverse is fine-tuned?

In his essay "The Argument to God from Fine-Tuning Reassessed," Richard Swinburne argues for rejoinder (a):

"...to postulate a large number of such universes as a brute uncaused fact merely in order to explain why there is a fine-tuned universe would seem the height of irrationality. Rational inference requires postulating one simple entity to explain why there are are many complex entities. But to postulate many complex entities to explain why there is one no less complex entity is crazy."

Theologian William Lane Craig likes to bring up (b). In this article, he refers to work by physicist Roger Penrose, which would suggest that there would be vastly more life-containing universes that were smaller than our own, and thus it would be much more likely that we find ourselves in a smaller universe.

"Roger Penrose of Oxford University has calculated that the odds of our universe’s low entropy condition obtaining by chance alone are on the order of 1:10^(10^123), an inconceivable number. If our universe were but one member of a multiverse of randomly ordered worlds, then it is vastly more probable that we should be observing a much smaller universe. For example, the odds of our solar system’s being formed instantly by the random collision of particles is about 1:10^(10^60), a vast number, but inconceivably smaller than 10^(10^123). (Penrose calls it “utter chicken feed” by comparison [The Road to Reality (Knopf, 2005), pp. 762-5]). Or again, if our universe is but one member of a multiverse, then we ought to be observing highly extraordinary events, like horses popping into and out of existence by random collisions, or perpetual motion machines, since these are vastly more probable than all of nature’s constants and quantities’ falling by chance into the virtually infinitesimal life-permitting range. Observable universes like those strange worlds are simply much more plenteous in the ensemble of universes than worlds like ours and, therefore, ought to be observed by us if the universe were but a random member of a multiverse of worlds. Since we do not have such observations, that fact strongly disconfirms the multiverse hypothesis. On naturalism, at least, it is therefore highly probable that there is no multiverse."

In light of Bostrom's analysis, response (a) is moot. It is perfectly reasonable to postulate a large number of entities if it makes the bayesian probabilities work out. The question is whether or not the prior improbability of a multiverse outweighs the explanatory benefit provided by a multiverse. Swinburne's position is based off of the assumption that the larger the number, the less likely it is there are at least that many universes. I'm not sure that we can say so much - we are talking about nature on a meta level, but we're bringing in considerations normally applied to smaller theories describing nature - but even if this is right, it still might not defeat the multiverse, if the probability that we exist given a multiverse is sufficiently greater than the probability that we exist if there is no multiverse (the latter probability is where considerations of design and other alternate hypotheses enter the equation).
As for Craig's analysis, I am not enough of an expert in physics to offer a direct response, except for the fact that many physicists still seem to think that a multiverse is entirely viable. But if it is in fact true that we are more likely to observe a much smaller universe given the existence of any multiverse, then a multiverse is indeed strongly disconfirmed. However, I think that the multiverse theory Craig refers to is very specific - Alexander Vilenkin's inflationary theory - and his considerations do not prevent us from thinking about other theories of the multiverse. Also, the examples he gives in the quoted paragraph are rather strange. Correct me if I'm wrong, but given the laws of physics, perpetual motion machines are mathematically impossible, not just very improbable. As for horses popping in and out of existence, I don't think that we should ever expect to observe such things, as I argued in the "digression" above: given that we observe any universe at all, even one that came into existence from a random collision of particles, it is still very improbable to then observe coherent objects popping in and out of existence due to random collisions. It's precisely the gambler's fallacy that past events affect future probabilities. Finally, I wonder what Craig means, precisely, by "small universe," and why he thinks we are not already living in one. If a solar system popped randomly into existence in a non-fine-tuned universe, I wonder how he expects life to be able to exist for a long enough time to weigh philosophical issues of existence. Ironically, if we found ourselves in a universe where all the laws of physics suggested that life should be impossible to occur evolutionarily, we would have a much better case for a design argument! So if God exists, we should expect to find ourselves in a universe not fine-tuned for evolution!
As for objection (c), I've already mentioned that multiverse argument are still more in the realm of philosophy rather than science, although they are consistent with and strongly hinted at by many theories of physics. Finally, (d): if it is true that a multiverse must be fine-tuned in its own way, then the argument is indeed self-defeating, lest it lead to an ensemble of multiverses (which might be acceptable to some). But I don't know of any special considerations which say that multiverses must be fine-tuned themselves. If we are making a philosophical inference anyway, we might as well infer the existence of a robust multiverse that doesn't require its own fine-tuning.

Conclusion

As with the Kalam Cosmological Argument, the fine-tuning argument is not a standalone argument for God, but rather one piece in a cumulative case for God - so even theists like Swineburne agree that it is a weak argument if we have no other reason to believe in God. The problem with the design hypothesis is its vagueness - what exactly does "design" mean? As Nick Bostrom briefly discusses, there are other design hypotheses that do not resemble the God hypothesis - for example, John Leslie's "causally efficacious ethical principle." And of course, there is the question of whether or not design causes a greater problem than it solves - wouldn't an eternal designer be more unlikely than the thing that it's fine-tuning? The explanation for this is, of course, that God is omniscient and omnipotent, and that these properties are in fact simple. But then we get into a whole new philosophical can of worms - in particular, how does a God go about creating something which does not exist in the first place? Designing a universe is not like designing a car: the materials for a car are preexisting; the materials for a universe are not.
The multiverse, with a little theoretical work, has the potential to neatly explain fine-tuning - but given the objections to it, I remain agnostic.
I can respect people who use fine-tuning to infer a single, simple entity as the cause of the universe - if you already believe in God for other reasons, you have no reason to doubt the plausibility of God being this cause. But the problem with explanations of this type, far from being an insufficient, is that they might be diagnosed as "magic." If I watch a magic show where the magician disappears from a locked box, I can either infer that a complicated series of preparations were made to perform the trick, or I can infer that the magician in fact has magic powers. The second explanation is obviously useless - but it is deceptively simple. After all, it only postulates one new entity, the magician's magic disappearing powers, with exactly the right explanatory power, whereas the "preparation" hypothesis requires a complicated mechanism with many parts!
The existence of the universe is an extraordinary mystery, one which may be ultimately impossible for us to crack. As Sam Harris put it, it's the only miracle worthy of the name. Sure, we can come up with multiverse and design theories of varying plausibility - but how extraordinarily presumptuous of us, to think that we can settle once and for all the question of why we are here on the basis of one data point (our universe). To do so would be to comprehend what for us is categorically incomprehensible: the nature of existence beyond space and time, beyond particles and fields, and beyond scientific testability. If we are to find God, we have no choice but to look for him in the light of the lamppost - it won't do to merely convince ourselves that he resides in the darkness.